Dr. Scott Gottlieb, former head of the Food and Drug Administration, on Tuesday shared how he plans to approach parenting this summer during the coronavirus pandemic.

Gottlieb, who has three children, told CNBC he would first be looking to make sure the virus is not spreading at "epidemic levels, which I hope we will be in the summer; I think we will be."

If that happens, "and my kids are otherwise fine — they're healthy, they don't have temperatures, they don't have colds — I'm not going to be concerned about them being around my parents, who are older," Gottlieb said on "Squawk Box." He also would allow them to play with friends.

"But I'm going to be more vigilant to make sure they don't have colds," said Gottlieb, a CNBC contributor who sits on the boards of Pfizer and biotech company Illumina. "If they do, then I'll probably keep them away because we know there's asymptomatic and mild illness here that could spread."

In general, people will need to "contemplate very carefully" decisions around interactions with people who are at a higher risk of getting seriously sick from Covid-19, Gottlieb said. That includes not just older individuals, but also people who are immunocompromised, he said.

Gottlieb said people will "have to start living our lives again," but he added he believes frequent hand washing, no handshakes and reducing "our travel where we can" will become routine behaviors. People may also get in the habit of frequently taking their temperature, he said.

"I think people are going to come out of this sufficiently concerned about the spread of this virus, that it is going to change behaviors in a way that are subtle for everyone but .. on the whole is going to reduce the risk of spread," he said.

With signs that daily increases in new coronavirus cases may be slowing, the national debate has moved in the direction of how the U.S. will reopen the economy. The Trump administration is expected to announce as early as Tuesday a new task force to evaluate that, as governors on the East and West coasts build coalitions to coordinate easing stay-at-home orders.

U.S. coronavirus cases were approaching 583,000 with 23,649 deaths, according to Johns Hopkins University data Tuesday morning. Global cases are nearing 2 million, with 120,450 deaths.

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There is a risk Covid-19 could come back in the fall if we don't have a vaccine: Scott Gottlieb